Without going into the legal and ethical problems that many binary brokers have gotten into, the biggest theoretical differences between forex and binary are:
a. In forex you determine when to buy/sell, based on what the market is doing at any given moment. In binary, it’s a pre-set time frame - either the asset goes up before teh trade expires, or it goes down.
b. In forex, the amount that you can earn (or lose) is completely dependent on when you buy/sell. The more pips the difference, the bigger the gain (or loss). In binary, whichever direction you guessed that the asset would move, whether it’s a one pip move or a 10,000 pip move, the amount at stake is the same.
c. Because of all this, forex gives you many more solid, long-term strategies to work with, and you can make decisions based on what the market is doing, or on what you believe it will do in whatever time frame.
There are some other differences, but these are, IMHO, the biggies.
Binary is more like “betting” than forex, but investing in forex IS still a bit of a gamble. But, anytime that you invest money in anything - stock market, buying a house, whatever - there is an element of risk, or “gamble” to it. The real question is how well do you learn what you’re doing before you take these risks. The more you know, and the more cautiously you approach forex (like any investments), the better chance you have of seeing a profit.
You can lose money if you buy a currency at one price, and the rate of exchange drops. For example, you spend 100 pounds to buy 132 US dollars when the GBP/USD rate is 1.32. If that rate drops, and you want to sell the dollars back when the rate is 1.25, you will get less money back than what you spent to begin with.